What I can't figure out is how the common denominator of 4a is gotten. Let me give an example. Lets say we want to add together 1/4 and 5/8. We would look of course at the multiples of 4 and find one that's equal to other denominator. So we find that 8 is the least common denominator for both fractions. We multiply 1/4 by 2/2 to get 2/8, and now we can solve.

Now lets look at -c/a. Any variable without a coefficient has an implied coefficient of 1 yes? So really we can look at -c/a as -1c/1a. How can we get a common denominator of 4 from 1, when 1 only has itself as multiple? This doesn't make sense to me. The only way I could figure it out was if both bases were the same, we could just say the fraction was equal to 1 and turn that into 1/2, therefore giving us the ability to get 4. Someone please explain this to me.

This is where I'm stuck. How do you get 4a/4a from the a in -c/a? Like I said in my original post, a variable without a coefficient has an implied coefficient of 1. So really -c/a is -1c/1a. How does 4a come from 1a? 1 only has itself as a multiple, where is the 4 coming from?

I'm not seeing a "4a/4a", and the "-c/a" appears to be unchanged between line 4 and line 5...?

Perhaps it would help if you reviewed this page which shows the step-by-step derivation of the Quadratic Formula, using the completing-the-square methodology, and then replied saying where in that process the explanation stops making sense. Thank you!

This is where I'm stuck. How do you get 4a/4a from the a in -c/a? Like I said in my original post, a variable without a coefficient has an implied coefficient of 1. So really -c/a is -1c/1a. How does 4a come from 1a? 1 only has itself as a multiple, where is the 4 coming from?

The simplest common denominator of the terms on the right hand side is 4a2. To add rational expressions, in this case you want to do this: